Practical corollaries of transverse Ward-Green-Takahashi identities

TL;DR

This paper explores the transverse Ward-Green-Takahashi identities in gauge theories, revealing new insights into how fermion-gauge-boson vertices are modified nonperturbatively, which is essential for understanding strong-interaction phenomena in the Standard Model.

Contribution

It provides a unified treatment and solution of both longitudinal and transverse Ward-Green-Takahashi identities, uncovering novel effects on dressed-fermion--gauge-boson vertices.

Findings

Derived new constraints on fermion-gauge-boson vertices.

Uncovered novel consequences for dressed-fermion interactions.

Enhanced understanding of nonperturbative vertex modifications.

Abstract

The gauge principle is fundamental in formulating the Standard Model. Fermion--gauge-boson couplings are the inescapable consequence and the primary determining factor for observable phenomena. Vertices describing such couplings are simple in perturbation theory and yet the existence of strong-interaction bound-states guarantees that many phenomena within the Model are nonperturbative. It is therefore crucial to understand how dynamics dresses the vertices and thereby fundamentally alters the appearance of fermion--gauge-boson interactions. We consider the coupling of a dressed-fermion to an Abelian gauge boson, and describe a unified treatment and solution of the familiar longitudinal Ward-Green-Takahashi identity and its less well known transverse counterparts. Novel consequences for the dressed-fermion--gauge-boson vertex are exposed.